I would start looking for a new water pump. There is a part missing that the fan bolts to, and the bolt through the pulley is not right. The 1 ton trucks used a 4 blade fan. Judging by the shroud in your picture, you must have a 1/2 ton or a car which should have a 2 blade fan. 

Here is a few pictures of what you should have.

I have a 1926 Chevrolet car and it has a 2 blade fan. The blades are bolted right to the fan pulley like in the photo I attached

@andy-somers-2  & @kenneth-hunkins    Thanks for the replies and pics.  I have a touring car.  Attached is a better photo of the shroud.  I was planning on a new water pump as it leaks a bit, and it looks like i also need a proper pulley.  My 4 blade fan looks like it comes apart.  If so, as it already fits in the shroud, and I'm thinking it would work as the 2 blade fan if the mounting holes line up on new pulley.

You can still use the 4 blade on a new waterpump. The part I thought was missing is bolted to your fan. The 1926 style pulley is not correct for your '28. I would write a wanted ad in this forum, i'm sure someone will have an extra they are willing to sell.

Andy

I understand that the fan and pulley are both pressed on to the shaft for a friction fit, although some pictures I have seen appear the show a nut at the end of the shaft.   Are there parts catalogues available that would show the proper assembly?

There appear to be 2 different length shafts available.  Which would be recommended?

@kenneth-hunkins 

Kenneth,   Your 26 water pump pulley is not correct  for 1926 .   looks like a 1932 pulley ?

If you are thinking of sourcing a new pump because of the fan flange remember there are two lengths of water pump in 1928. A shrt one for the trucks, and a longer one for the cars.